# compute.sigma.star: Computes intermediate (tetrachoric) correlation matrix In BinNor: Simultaneous Generation of Multivariate Binary and Normal Variates

## Description

This function computes the intermediate correlation matrix by combining tetrachoric correlation for binary-binary combinations, biserial correlations for binary-normal combinations and Pearson correlation for normal-normal combinations. If the resulting correlation matrix is not positive definite, a nearest positive matrix will be used.

## Usage

 ```1 2``` ```compute.sigma.star(no.bin, no.nor, prop.vec.bin = NULL, corr.vec = NULL, corr.mat = NULL) ```

## Arguments

 `no.bin` Number of binary variables `no.nor` Number of normal variables `prop.vec.bin` Probability vector for binary variables `corr.vec` Vector of elements below the diagonal of correlation matrix ordered columnwise `corr.mat` Specified correlation matrix

## Value

 `sigma_star` A resulting intermediate correlation matrix Σ^* `nonPD` If a resulting intermediate correlation matrix is non-positive definite, it is stored in this value. Otherwise it is NULL. `PD` TRUE if Σ^* is positive definite, FALSE otherwise. A FALSE indicates that the nearest positive definite matrix is returned. `eigenv` Eigenvalues of the Σ^* before the conversion

`validation.corr`, `nearPD`, `phi2poly`, `is.positive.definite`,
`jointly.generate.binary.normal`, `simulation`
 ```1 2 3``` ```cmat = lower.tri.to.corr.mat(corr.vec= c(0.16, 0.04, 0.38, 0.14, 0.47, 0.68),4) compute.sigma.star(no.bin=2, no.nor=2, prop.vec.bin=c(0.4,0.7), corr.vec=NULL,corr.mat=cmat) ```